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Abstract

A simple and general approach for designing practical all-optical (all-fiber) arbitrary-order time differentiators is introduced here for the first time. Specifically, we demonstrate that the Nth time derivative of an input optical waveform can be obtained by reflection of this waveform in a single uniform fiber Bragg grating (FBG) incorporating N π-phase shifts properly located along its grating profile. The general design procedure of an arbitrary-order optical time differentiator based on a multiple-phase-shifted FBG is described and numerically demonstrated for up to fourth-order time differentiation. Our simulations show that the proposed approach can provide optical operation bandwidths in the tens-of-GHz regime using readily feasible FBG structures.

Figures (10)

Fig. 2. Amplitude (solid, red curve) and phase (dashed, blue curve) of the reflection spectral response of a FBG with two symmetrical π-phase shifts (parameters given in the text). For comparison, the amplitude spectrum of an ideal second-order differentiator is also represented (dashed, magenta curve).

Fig. 6. Amplitude (solid, red curve) and phase (dashed, blue curve) of the reflection spectral response of a FBG with three π-phase shifts properly located to achieve third-order optical differentiation (parameters given in the text). The solid, cyan curve shows the amplitude reflection spectrum of a FBG with three symmetrically located π-phase shifts designed according to the conditions derived for second-order differentiation. For comparison, the amplitude spectrum of an ideal third-order differentiator is also represented (dashed, magenta curve).

Fig. 9. Amplitude (solid, red curve) and phase (dashed, blue curve) of the reflection spectral response of a FBG with four symmetrical π-phase shifts (parameters given in the text). For comparison, the amplitude spectrum of an ideal fourth-order differentiator is also represented (dashed, magenta curve).